Question

which statement describes the graph of the system of equations below?\\(1.5x + 0.2y = 2.68\\)\\(1.6x + 0.3y = 2.98\\)\\(\bigcirc\\) the lines are parallel.\\(\bigcirc\\) the lines overlap at all points.\\(\bigcirc\\) the lines intersect at \\((1.6, 1.4)\\).\\(\bigcirc\\) the lines intersect at \\((3.1, 0.5)\\).

Explanation:

Step1: Write given equations

$1.5x + 0.2y = 2.68$
$1.6x + 0.3y = 2.98$

Step2: Eliminate y via scaling

Multiply first eq by 3: $4.5x + 0.6y = 8.04$
Multiply second eq by 2: $3.2x + 0.6y = 5.96$

Step3: Subtract scaled equations

$(4.5x + 0.6y) - (3.2x + 0.6y) = 8.04 - 5.96$
$1.3x = 2.08$

Step4: Solve for x

$x = \frac{2.08}{1.3} = 1.6$

Step5: Substitute x to find y

$1.5(1.6) + 0.2y = 2.68$
$2.4 + 0.2y = 2.68$
$0.2y = 2.68 - 2.4 = 0.28$
$y = \frac{0.28}{0.2} = 1.4$

Answer:

The lines intersect at (1.6,1.4).